Question 630723
I've corrected the given from 68.3 to 683meters.<br>

For the illustration please see this (placed on my fb profile)
https://www.facebook.com/photo.php?fbid=3633779889920&set=a.1100830367765.2014805.1436862519&type=1&relevant_count=1&ref=nf

<pre>
Solution:
(a) Let d = depth of water @ galleon's location
 Use sine of angle of depression = opposite / hypotenuse.
 </pre>  
     sin 27°52&#8242;=d/683
     d = 683sin 27°52&#8242;         ---> Multiply both sides by 683.
     d = 319.24 meters               --->Ans. depth of water @ galleon's location
<pre>



(b) Let x = distance the ship would sail to be directly above the galleon
 Use cosine of angle of depression = adjacent / hypotenuse.
 </pre>  
cos 27°52&#8242;=d/683
     x = 683cos 27°52&#8242;         ---> Multiply both sides by 683.
     x = 603.8 meters               --->Ans. distance the ship would sail to be directly above the galleon
<pre>



(b) Let angle B = angle of depression of the galleon when the ship has gone 520 m
 Use tangent of angle of depression(angle B) = opposite / adjacent.
  </pre> 
tan (angle B) = d/x-520
tan (angle B) = 319.24/(603.8-520)   &nbsp;&nbsp;&nbsp;      ---> Solved from (a)d=319.24 and (b)x=603.8
(angle B) = arctan (319.24/83.8)     &nbsp;&nbsp;&nbsp;      ---> Get arctan of both sides.

(angle B) = 75.29° or 75°17&#8242;   &nbsp;      ---> Ans. angle of depression of the galleon when the ship has gone 520 m
<br>
Answers;
(a) depth of water @ galleon's location = <font color=red>319.24 meters  </font> 
(b) distance the ship would sail to be directly above the galleon = <font color=red>603.8 meters</font>
(c) angle of depression of the galleon when the ship has gone 520 m=<font color=red> 75.29° or 75°17&#8242;</font>
God bless. Email me- rmnavalta@yahoo.com